Logic and Applications

Looking at the new gaming table we need to address the problem of card counting. This has been an issue over the past years and to eliminate it we need to understand how counting can be done in the first place. Counting cards is being able to track the relationship between the high valued cards and the low. The strategy with this is to be able to play as others do without being recognized as a counter. By this I will use the poker face, many will hem and haw over their decisions and a well groomed counter can do this without being noticed by others. What is needed is one that can see the faces of the players and calculate how their expressions play into the game. A way to be able to read faces is to learn how to count cards yourself. Having the basic strategy and understanding will help to develop one into seeing into the future of players. We can go further with this and develop a dealer who can spot a player of this caliber more easily if they understand statistics along with full on counting skills.
At this time we need to have a group of people and begin training them to count cards. By doing this along with teaching a statistical aspect of the problem we can begin to have dealers who are able to spot basic card counters at a glance. For training we will use High-Low, this will help to train at a faster rate.
High-Low the 2-6 are valued at +1, and the 10s and Aces are counted as -1. Note that there are the same amount in each group: 2,3,4,5,6 and 10,J,Q,K,A. The 7,8,9 are neutral in this count. An eye should be trained to not even see these for counting purposes, for they have no bearing on the count. Start with a deck of cards, flipping them over one at a time and keeping the running count. If they come out 8,K,3,3,6,2,7,A we would count 0,-1, 0, +1, +2, +3, +3, +2. At the end of the deck we should come out at "0". Continuing to practice this we can…...

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...Logic Application
With this game the players are card counting in a since. It’s a process of elimination. They know what is in there hand and a card that is in the opponents hand. Knowing that there are cards numbered from 1-9 you start by taking out what is in your hand and the cards that are located on each person’s forehead. Then listening to key questions you will be able to come up with an answer. So Andy draws the first question:
Andy draws the question card, “Do you see two or more players whose cards sum to the same value?” He answers, “`yes.”
Sum of Belle's cards = 5 + 4 + 7 = 16
Sum of Carol's cards = 2 + 6 + 4 = 12
Since these have different sums, but Andy sees at least two players whose cards have the same sum, then your cards must add up to either 12 or 16
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Next Belle draws the question card, “Of the five odd numbers, how many different
Odd numbers do you see?” She answers “All of them.”
The only odd cards that Belle sees from Andy and Carol are 5, 7
So you must have 5 and 7
--------------------
5 + 7 = 12
You know that sum of your cards = 12 or 16
Since 5 + 7 = 12, and smallest card is 1, then your cards must add to more than 12
Sum of your cards = 13
Third card = 13 - 7 - 5 = 1
Your cards: 1,5,7
So if a person listens to the clues that that are being asked and applies those questions to what they already know with what the hold in there hand they will be able to come up with the unseen card that...

...Assignment 1 The Logic Application
Dr. Keva Yarbrough
Detra Lawrence
Math 104
February 27, 2013
Assignment 1 The Logic Application
One of the greatest strengths in math is it concerns with the Logic proof of its given proposition. Any Logical system must start with some undefined terms, definition, and axioms. There are many ways you can analyzed certain numbers or statistics. In this essay, we learned the outcome solving problems using concepts from the set theory and logic of the situation.
This is a game call Guess Your Cards which is played by four players. Each player has to draw three cards 1 through 9 dealt face down and then places it on their heads so that everyone but the player can see the cards. We find that Player 1 Andy has won the game by answer to the card from the question deck. By the given information Andy has a sum of 13. Belle has a sum of 16. Carol has the sum of 12. Since Andy question was “Do you see two or more players with same value,” he replied yes. Belle question was asked “out of the five odd numbers do you see all different odd number,” she replied saying I see all odd numbers. Andy is the only player who Belle sees who has odd number of cards which is 1, 5, and a 7 which leads player 4 with the missing odd numbers of a 3 and 9. Since 3 and 9 sums to 12, and player 4 is missing its third card this lets us know player 4 number will value to Belle sum which is 16 and player four will have a 4 as its third card. With all......

...Assignment 1: Logic Application
Andy, Belle, Carol, and I are playing the game Guess Your Card. In the game, each person draws three cards without looking from a stack of cards containing contain multiple cards ranging in denomination from one to nine. Each person then places the cards on his or her forehead so that all of the other players can see the others’ cards, but cannot see their own. There is also a stack of questions that each person draws from in turn. These questions help the players deduct the identities of their own cards.
We have shuffled the deck and each player has drawn three cards and placed them on their own forehead. Andy has drawn 1, 5, and 7; Belle has drawn 5, 4, and 7; and Carol has drawn 2, 4, and 6. Obviously I cannot see my own cards. Andy draws the first question, which asks, “Do you see two or more players whose cards sum to the same value?” To which he answers, “Yes.” Belle’s turn is next. Her card asks, “Of the five odd numbers, how many different ones do you see?” She responds, “All of them.”
With these two questions, I am able to deduce which cards I have. After Andy drew the first question, “Do you see two or more players whose cards sum to the same value?” I added up Belle’s and Carol’s cards to see if theirs sum to the same total. Belle’s cards (5,4,7) add up to 16. Carol’s cards (2,4,6) add up to 12. Since Belle’s and Carol’s cards do not add up to the same amount, I can conclude that my cards add up to either 16 or 12. The next......

...which he answered “Yes” . Andy’s cards sum to 13, Belle cards sum to 16 and Carol’s cards sum is 12. Therefore my cards must equal the sum of one of those numbers. My cards cannot sum to 12 like Carol’s because I need to have a third card on my head, so therefore my cards must equal 13 or 16. My cards cannot equal the sum of 13 because Andy said that he has a 1, 5, and a 7 on his head because he does not see a 1 on anyone else’s head. Therefore the remaining cards on my head must be a 4 to sum to 16 the same as Belle’s. The cards that I have are 3, 4, and9 which is the equal the sum of 16.
You just have to use logic when handing out the playing card’s realizing that you are working with number 1 to 9 you have even and odd numbers that you are playing with. You can see your opponent’s cards but not yours it’s all about thinking and using logic. The logic is “Process of elimination”, with more possibilities being eliminated every time new information comes up for a different player....

...Assignment 1: Logic Application
I am playing “Guess Your Cards” with Andy, Belle, and Carol. Andy has drawn a 1, 5 and 7, Belle a 4, 5 and 7, and Carol a 2, 4 and 6. No one can see their own cards. Question cards are drawn and asked to help each player deduce what their own cards are.
I believe deductive reasoning would be the logic used to solve this problem; you have the facts in front of you. The deck has only cards with the numbers 1 through 9 on them, you can see the cards already drawn and deduct, by the answers to the questions, exactly what cards you have.
Let’s start with the first question. “Do you see two or more players whose cards sum to the same value?” Andy answers “yes”. Of the cards I can see, no two people have the same sum. I deduce that I must have the second set. Adding the cards of each person, I can see that Andy’s cards equal 13, Belle’s equal 16, and Carol’s equal 12. My set of cards must equal one of these.
Second, “Of the five odd numbers, how many different odd numbers do you see?” Belle answers that she sees all of them. I can only see 1, 5, and 7. Therefore, I must have a 3 and a 9. These are the only two odd numbers that I cannot see.
The statement that Andy knows what cards he has is totally irrelevant to the problem. It has absolutely no bearing on my logic or what cards I have.
Knowing I have a 3 and a 9, I only have to figure out what my last card is. My 3 and 9 add up to 12, therefore, my sum cannot to be equal to Andy or Carol......

...Phylicia Charles
Instructor: Dr. Abed Almala
MAT 104: Algebra with Application
December 4, 2011
The problem
What cards do I have in a guessing game with each card labeled one through nine? This game is being played with three friends and we can only see what each other have since when we draw the cards it goes on our heads without us seeing what we draw. We have to use logic and math to figure what card(s) we have on our heads.
The approach
I would use inductive reasoning to solve this problem. This would allow me to logically reason and reach conclusions based on the observations. This means I can look at the cards on my friends head, calculate how much of each number is present in the deck and probability that of me drawing one of the same card my friends have or a different card. In this game I would be using a lot of conjecture; because the evidence is uncertain or incomplete.
Conclusion
The recommended course of action was to use logic. The type of logic I recommend and used was inductive .Inductive reasoning was useful by using conjecture to find out what cards I had on my head. Another recommendation is to know the amount of each number so that I was able to calculate the probability of drawing a card that one of my three friends has or entirely different cards. I was able to generalize by making individual observation by paying keen attention to my three friends.
Solutions Details
This would be solved for example there are 4 of......

...“Of the five odd numbers how many of them do you see? “ Since Belle cannot see her cards, Carol has a 2, 4, and 6 so she is eliminated that leaves Andy and myself. Andy has a 1, 5, and 7 which is three of the odd numbers, so using a simple process of elimination two of my cards must be 3 and 9. Now going back to Andy’s question, since he cannot see his own cards and two of the players he saw had equal sums it is impossible for me to have the same sum as Carol because it is 12 and I already have the sum of 12 with only 2 cards. Therefore my sum has to be the same as Belle which is 16, since I have a 3 and a 9 which equals 12, so 16 minus 12 equals 4 which is my missing card. So Anthony’s cards are 3, 4, and 9. This is an example of simple logic and required absolutely no reading from the textbook, everything is answered in the within the assignment situation all you have to do is read it....

...The salient facts presented in Assignment #1 consist of listing the cards of three players while playing the Guess Your Card game, in which the student, as the fourth player, must guess his/her cards. Each player receives (3) cards numbered 1-9 and can see every other player’s cards, but not their own cards. By drawing questions, each student must figure out their own cards based on the answers provided by the other players and based upon the cards he/she can see. In this Assignment, players and their cards are as followed: Andy has 1, 5 and 7; Belle has 5, 4 and 7; Carol has 2, 4 and 6; and the final player’s cards are to be determined. Based on questions answered, two players have cards that total the same sum and all odd numbers 1-9 are included in this round of play.
My strategy for solving the problem was based on the process of elimination. As the fourth player, based upon the cards that I can see, as well as, the answers to the questions asked, I am able to determine that the sum of my cards is the same as the sum of another player. I am also able to determine that my cards include two odd numbers not presented by any other players. By process of elimination, I am able to determine my last card as well.
Andy answers “yes” to the question, “Do you see (2) or more players whose cards sum to the same value?” My first step in solving this problem was to add up all the card sums of each player. The sum of Andy’s cards is 13; the sum of Belle’s cards is 16; and...

...Logic and Application Card Game
MAT/104 Algebra with Applications
Marisol Rivera
Professor Russell Sundberg
October, 15,2013
Logic and Application Card Game
Name of the game Guess your 3. Guess your 3 is America new popular family game. Takes 36 Cards have number between 1 and 9 ... Add 2 to 10 player ages 7 to adults... plus extremely easy rules for teams or individuals ... And what do you have?... An hour or an entire evening entertainment using Logic and application.
Content
36 cards with number between 1 and 9
12 Question card
10 head ring to hold cards.
Objective
Be the first player to Guess what your 3 card are. First person to do this correctly wins.
Setup
1. Each player draws (3) cards (Without Looking). Each player will have numbers between 1 and 9.
2. The player then place their card on the head ring, so that everyone but the player can see the cards.
3. Place the deck of question in the center. Players will answer question based on the card that He or She selects.(Note: Not the player 's card , which the player cannot see) Example Tim draws a questions card, "How many 7's do you see?" he answered ,"one" because he cannot see the 7 on his heads he could only see the 7 on another player.
Now that we know the games content, objective and how to setup , Let's play. In this round there will be 4 players, Andy, Belle, Carols, and Marisol. Following the direction all 4 players draw 3 cards without looking, every player knows that each card......

...Logic Application
Jessica Mitrov
Mat/104
October 28,2013
Rami Hanbali
Logic Application
We are given an illogically logical problem. When reading the clues that we are given it makes no sense what so ever. I read the problem multiple times and no matter what way I read it there never seemed to have any logic to it. So I will show you the important facts that were given to us, the strategy I used, I will also give you a blow by blow on how to solve the problem, and finally tell you the answer to how Andy figured out what his cards were. By the end of this paper you will see how this illogical problem actually is a very logical problem.
The most important information that is given to you in an indirect way is that you have to find the missing information to make the illogical problem become logical. You are told that you plus three other people have cards with numbers anywhere between one and nine. You are given the numbers to Andy, Belle, and Carol. They also tell you that Andy sees two people that have cards that have the same sum, and that Belle sees all of the odd numbers between one and nine.
Now that we know the information that we found out that the problem makes no sense our strategy is to use logic and deductive reasoning. In order to do that you have to find out what your three cards are. Once you know that then the answers to the two questions will make since, and from there you will be able to figure out how Andy was able to guess what his cards are. So......

...Week 3 Assignment 1: Logic Application
James R. Johnson
Professor Robert Grier
Math 104
24 October 2013
I am playing Guess Your card with Andy, Belle, and Carol. The point of this game is to guess what cards you have and the first to accomplish this wins. Each player has to draw three cards without looking and place them on their heads. The cards have a number on them between 1-9. During each play, the players have to draw a question from the questions deck. The player then answers the questions based on what they see.
During the game, Andy draws 1, 5, and 7. Belle drew 5, 4, and 7. Carol drew 2, 4, and 6. Andy’s question card asks if he sees two or more players whose cards sum to the same value. He replies, “Yes.” Belle’s draws a question card asking, “Of the five odd numbers, how many do you see?” See says all of them. Andy then states, “I know what I have.” “I have 1, 5, and 7.”
Even with the given information, I still don’t know my card numbers. I will solve this problem by finding the terms not given. Based on the variables I do have, we know that Andy and myself have all the odd numbers because Carol’s numbers are even. Andy has 1, 5, and 7, which leave 3 and 9 with me. By referring back to Andy’s question, we are able to find that my remaining number is 4. I’m able to find this out because Belle’s numbers total 16, Carol’s numbers total 12, and my to given numbers are 3 and 9. The only number that could be my third number and total 16 is......

...I am playing a Guess your card game with 3 other people. Andy, Belle, Carol, and myself all draw three cards without looking. Each card has a number from 1-9 on it. We each drew 3 cards: Andy got cards 1, 5, and 7. Belle has the cards 5, 4, and 7, and Carol has the cards 2, 4, and 6. I’ll be using logic and the process of elimination to figure out what cards that I have. Also to see how Andy figured out his cards. Andy draws the question card, “Do you see two or more players whose cards sum to the same value?” He answers “Yes.”
Sum of Belle's cards = 5 + 4 + 7 = 16
Sum of Carol's cards = 4 + 6 + 2 = 12
The sum of Belle’s cards is 16 and Carol’s sum is 12. Thats means the sum of my cards must be 16, or 12. Next Belle draws the question card, “Of the five odd numbers, how many different odd numbers do you see?” She answers, “All of them.” If Belle sees all five odd numbers she sees 1,3,5,7, and 9. I can only see 3 different odd numbers so I must have the other 2 odd numbers that Belle can see. The remaining odd numbers that I must have are 3 and 9. Since the sum of 9 and 3 is 12 that is already the sum of what Carol has.The smallest 3rd number can only be 1. So I must have a sum of 16. My 3rd number must be a 4. The total sum of my cards is now 16, same as Belles. Now you see why Andy knew what cards he had. He realized that the only odd numbers Belle could see from Carol and I were 3 and 9, and yet she claimed she could see all five odd numbers. So the remaining three:...

...Logic Application Project
Written By: Mrs. Tangela Wright
Professor: Ms. Terry Clark
Course Title: Algebra With Applications
Date: March 2, 2012
The question that has been asked to be solved during this logic application project is as follows: “ What Cards do I hold.” In completing the answer to this question one must remember the following “ An Experiment is an observation on any physical occurrence. The sample space of an experiment is the set of all it’s possible outcomes.” I must say that since I am not a person that enjoys playing card cards. I would have to look at this information the same way that I would look at and have taught my daughter (9) to play Domino’s.
In solving this problem one most look at all the information that has been provide and be sure to write this information on paper so that you will be able to look at the complete picture and us the variables that have been provided in order to solve the problem. One can say that the strategy to solving this problem could be one of two methods. You could use “Process of Elimination” or Probabilities of Unions and Intersection new information has been reveled about the cards that the other players have. You would need to keep that information in mind and use it to solve the situation to uncover that cards that you may be hold just like in the 1st example.
My conclusion as to what cards, I have in this game of chance are the following 5, 9 and 4. I am able to get to this...

...Logic Application
Michael Minor
Strayer University
Mat104
March 7, 2012
Dr. Raymond Chen
I am playing a game of Guess Your Card with three other people. The cards are numbered 1 through 9 and each player is dealt three cards face down. Each player then places their cards on their heads so everyone but themselves can see their cards. From my perspective, Andy has the cards 1, 3, and 7; Belle has the cards 3, 4, and 7; and Carol has the cards 4, 6, and 8. We all must determine what cards are on our heads by the answers to the cards from a deck of questions. Andy draws the question “Do you see two or more players whose cards sum to the same value?” to which he answers “Yes.” Since the sum of Belle’s cards is 14 and the sum of Carol’s cards is 18, this tells me that my cards add up to either 14 or 18. Belle draws the question “Of the five odd numbers, how many different odd numbers do you see?” and answers “All of them.” This tells me that I have a 9 and a 5 on my two of my cards since I can only see a 1, 3, and 7 from my viewpoint. Since I must have a sum of either 14 or 18 on my cards and 9+5=14, I can deduce that the total sum of my cards must be 18 and my final card must be a 4....

...Logic Application
Shannon Will
Professor Taylor
Algebra with Applications
May 31, 2012
I am playing “Guess Your Cards” with Andy, Belle, and Carol. Andy has drawn a 1, 3 & 7, Belle a 3, 4 & 7, and Carol a 4, 6 & 8. No one can see their own cards. Question cards are drawn and asked to help each player deduce what their own cards are.
I believe deductive reasoning would be the logic used to solve this problem; you have the facts in front of you. The deck has only cards with the numbers 1 through 9 on them, you can see the cards already drawn and deduct, by the answers to the questions, exactly what cards you have.
Let’s start with the first question. “Do you see two or more players whose cards sum to the same value?” Andy answers “yes”. Of the cards I can see, no two people have the same sum. I deduce that I must have the second set. Adding the cards of each person, I can see that Andy’s cards equal 11, Belle’s equal 14, and Carol’s equal 18. My set of cards must equal one of these.
Second, “Of the five odd numbers, how many different odd numbers do you see?” Belle answers that she sees all of them. I can only see 1, 3, & 7. Therefore, I must have a 5 and a 9. These are the only two odd numbers that I cannot see.
The statement that states that Andy knows what cards he has is totally irrelevant to the problem. It has absolutely no bearing on my logic or what cards I have.
Knowing I have a 5 and a 9, I only have to figure out what my last card...